When the measured apparent resistivity varies a lot with spacing, a uniform soil gives unreliable results. IEEE 80 proposes a two-layer model: a top layer of finite thickness and an infinite bottom layer, with different resistivities, related by a reflection factor K. The two-layer model is more accurate, and the equivalent uniform soil is kept for moderate variations.
Short answer. Soil resistivity is almost never the same from the surface to depth. When measurements show that apparent resistivity changes a lot with electrode spacing, IEEE Std 80-2013 recommends moving from a uniform soil to a two-layer model: a top layer of finite thickness over another of infinite thickness, each with its own resistivity. It is an approximation, but closer to reality, and the guide considers it sufficient in most cases to design a safe grounding system.
Why a uniform soil is not enough
The guide’s equations for step and mesh voltages assume uniform soil. But, according to clause 13.3, a site with uniform resistivity over its whole area and to great depth is rare. There are normally several layers, each with a different resistivity, and sometimes lateral changes too, although more gradual.
Clause 13.4 admits that interpreting the apparent resistivities from the field is perhaps the most difficult part of the measurement program. The goal is a model that closely approximates the real soil; the guide recognizes that a perfect fit is unlikely. The most common models are the uniform and the two-layer, and multilayer models are used in more complex conditions. Field data collection is covered in resistivity measurement with the Wenner method.
The equivalent uniform model
A uniform model can be used when the variation of apparent resistivity is moderate and no tools for two or more layers are available. As a first approximation, or to get an order of magnitude, the guide calculates a uniform resistivity by averaging the apparent resistivity measurements (equation 52). A second value, the average of the maximum and minimum measured values (equation 53), gave results comparable to those of the two-layer model in the soils analyzed in Annex E.
The guide sets two conditions on the second value: it is not recommended for a grid without rods, and the rods must reach at least the depth where the measured resistivity corresponds to that value. It also warns that the equation must be used with care because of the assumptions of the study.
Another criterion cited is to use the average apparent resistivity of the top layer for step and touch voltages, and that of the bottom layer for the resistance of the system.
The two-layer model
It consists of a top layer of finite thickness over a bottom layer of infinite thickness. The abrupt change of resistivity at the boundary is described by the reflection factor K:
K = (ρ₂ − ρ₁) / (ρ₂ + ρ₁) (equation 54)
where ρ₁ is the resistivity of the top layer and ρ₂ that of the bottom layer, both in Ω·m. K ranges between −1 and 1. It is positive if the upper layer is less resistive than the lower one, and negative in the opposite case.
The guide notes that, in most cases, representing the soil with an equivalent two-layer model is enough to design a safe grounding system. The parameters (ρ₁, ρ₂ and the height h of the top layer) are obtained from the measurements by manual or graphical methods or with programs. When a two-layer model is not enough, for example with minima and maxima in resistivity, multilayer models with computer techniques are used.
An example from the guide
In the Sunde graphical method of clause 13.4.2.2, the starting point is the curve of apparent resistivity against spacing. In the example, with the curve of soil type 1, ρ₁ = 100 Ω·m and ρ₂ = 300 Ω·m are estimated. The ratio ρ₂/ρ₁ is 3, and with the Sunde chart a top-layer height of about 7.0 m is obtained. With the EPRI TR-100622 program the result is 6.1 m. That is good agreement for a manual method.
What changes in the grid depending on the model
A grounding system behaves differently in two-layer soil than in uniform soil. Clause 13.4.2.3 summarizes it as follows:
| Situation | Effect |
|---|---|
| Negative K (more resistive top layer) | Grid resistance is lower than in a uniform soil of resistivity ρ₁. Step and touch voltages are usually lower. Current is shared more evenly among the conductors, because it tends to go down toward the less resistive layer |
| Positive K (less resistive top layer) | Resistance is usually higher than in uniform soil of resistivity ρ₁. Step and touch voltages are usually higher. Current density is higher in the edge conductors |
| Top layer much thicker than the electrode | The electrode behaves as in a uniform soil of resistivity ρ₁ |
The guide warns that these trends assume a constant current source, and that the actual current changes with ρ₁ and ρ₂ because of current division. For large-area designs, irregularly shaped grids or clearly very non-uniform soils, the design engineer decides whether more sophisticated methods are needed.
How it relates to tolerable voltages
Two-layer soil also comes into the surface layer. When the surface material is more resistive than the soil, the Cs factor reduces its effect; but if the top layer were less resistive than the one below, that factor does not apply and the problem is solved with a multilayer soil analysis (clause 7.4).
We do your grounding study
We interpret the resistivity measurements of your site, define the soil model that applies and calculate the grid with it. If you already have measurements, we review them before using them. For a first estimate you can use our free grounding resistance tool, which fits a two-layer model to your Wenner readings in the “Resistivity” tab and warns when the measurements vary a lot. The model assumes point test electrodes and a bottom layer without a floor, and does not suit soils of three or more layers. See our engineering design and studies service or write to us through contact.
Related guides
- IEEE 80: Substation Grounding Safety
- Soil Resistivity Measurement: Wenner Method
- Gravel Surface Layer in Substations: Cs Factor and Safety
- Grounding Grid Resistance: IEEE 80 Formulas
- Ground Resistance Test: Fall-of-Potential and IEEE 81
References
- IEEE Std 80-2013, IEEE Guide for Safety in AC Substation Grounding: clauses 13.3 and 13.4 (interpretation of measurements; equations 52 to 54), 13.4.2.2 (Sunde graphical method), 13.4.2.3 (comparison of uniform and two-layer soil), 7.4 (surface layer) and Annex E (equivalent uniform soil model).
- EPRI TR-100622, program for two-layer soil models, cited in IEEE Std 80-2013.
- S. Sunde, Earth Conduction Effects in Transmission Systems (1968), cited in IEEE Std 80-2013.
Frequently asked questions
When is a uniform soil model enough?
IEEE 80 says it should be used only when the variation of apparent resistivity is moderate. In truly homogeneous soils, which rarely exist, it can be reasonably accurate. If the measured variation is large, it is unlikely to give accurate results.
What does the sign of the reflection factor K tell you?
K is positive when the top layer is less resistive than the bottom one, and negative when it is more resistive. With negative K, the grid resistance and the step and touch voltages are usually lower than in a uniform soil with the resistivity of the top layer; with positive K they are usually higher.
Are two layers always enough?
No. If the resistivity variation has maxima and minima, an equivalent two-layer model may not be accurate. In those cases the guide says a multilayer model may be required, solved with computer programs.